In a dig at judges who have questioned the SEC's rules and its historic practice of allowing firms to settle cases without admitting wrongdoing, Ms. White suggested the courts were acting beyond the scope of their roles and should instead "defer to the agency's reasoned judgments."

"We recognize that, under the law, a court can review a settlement," she said, in prepared remarks at Fordham Law School. "But a court that reviews a settlement that a law enforcement agency like ours enters with a defendant has a more limited task."

Though she didn't refer to him by name, her remarks appeared to be criticism of U.S. District Judge Jed S. Rakoff for rejecting a proposed 2011 deal allowing Citigroup Inc. to pay $285 million to settle allegations the bank misled investors in a 2007 mortgage-bond deal. Mr. Rakoff said allowing companies to settle charges without admitting or denying wrongdoing is "hallowed by history, but not by reason."

After Ms. White said "I will not speak of any specific cases, or ill of any of my judicial friends," she paused, and to laughter from the audience, said, "Who am I talking about?" She then appeared to look in the direction of where Judge Rakoff was sitting.

Ms. White, who took over the SEC in April, has changed the agency's long-standing settlement policy and said it would insist on admissions of wrongdoing in certain cases of egregious offense, harm to investors or where public accountability is needed. But Ms. White suggested the shift was prompted by her background as a federal prosecutor and not by judicial criticism.

"The core decision as to whether to seek admissions is a decision for the commission to make in its best, independent judgment of what should be required," she said.

Speaking earlier Thursday, Ms. White said her prior legal work representing large banks and securities firms was "invaluable" in laying out a tougher enforcement policy that includes the pursuit of admissions of wrongdoing in certain cases.

"I realized just how much leverage the SEC has," Ms. White said, speaking at the Women, Influence & Power in Law summit in Washington. Many companies would sooner acquiesce to a demand for an admission than engage in a long dispute with the agency, she said. "You don't want to be at war with your main regulator," she said.

In her remarks at Fordham, she also took aim at several provisions of the 2010 Dodd-Frank law, including one that requires companies to report their use of some minerals sourced from Africa, all but saying they were inappropriate. The provisions, she said, "seem more directed at exerting societal pressure on companies to change behavior, rather than to disclose financial information that primarily informs investment decisions."

"That is not to say that the goals of such mandates are not laudable," she said. "But, as the chair of the SEC, I must question, as a policy matter, using the federal securities laws and the SEC's powers of mandatory disclose to accomplish these goals."

The agency is also grappling with questions surrounding financial wizardry such as dark pools and high-frequency trading. The extent of the benefits and harms to investors aren't fully known, Ms. White said, and the agency is releasing data that will "show how the markets are operating" and what the impact of speed actually does to the markets. The agency will seek input on the data, she said.

Asked whether the exchanges and big brokerages could withstand a major cyberattack, Ms. White said such attacks are "obviously of concern" and that "there's a lot of attention being paid to that," and an "awful lot" of time, though "less so in the SEC space." Ms. White said the agency is making disclosures so that "everyone's informed of the range of attacks that are occurring."